conservation of angular momentum, whip physics, and a serve question

Ok, so first an observation I've made regarding how to serve properly. I've often heard it said that the shoulders should be square with the net at the same time that the arm reaches full extension. The idea is that alignining the timing of the shoulder/chest turn with the timing of the arm extension allows for most efficient power transfer to the ball.

One of the posters here (jollyroger) even posted side by side comparison photos of his serve vs. another poster's serve which illustrated this beautifully.

This makes intuitive sense, however it seems (at least on the face of it) to contradict a principle of whip cracking.

One of the things that allows the kinetic chain to manifest such high speeds is the conservation of angular momentum. Suppose you have three straight pieces of wood, and you connect them together end by end, but allow them to rotate within a certain range of motion. They can rotate 180 degrees in one direction, but once they align up with each other, they cannot rotate any more.

See picture below:

The dashed lines indicate the limits of the "joint angles".

Now suppose the black portion weighs more than the blue portion, and the blue portion weighs more than the red portion.

We can now crack this whip as follows:

We simply rotate the heavy black handle, and then allow the momentum to channel to the next link (the blue one). If the black handle stops moving, all that momentum gets channeled to the blue link. But because the blue link is lighter, it will move faster than the black one did, due to conservation of momentum (mass * velocity). By the time the red one moves independently (due to the black and blue one having reached their joint limits), it's much faster than the original black one.

This principle can be used in cracking the whip of the arm, but my question is whether it should also be used to channel momentum from the torso to the arms.

If so, then wouldn't it make sense to have the shoulders and chest square with the net/target before the arm starts to crack? So long as you prevent the torso from overrotating, and "apply the brakes", then that momentum will be channeled into the arm.

Why doesn't serve instruction encourage this delayed cracking of the whip principle between torso and arms?

According to the paper, and this "whip physics" which does apply to serves by the way, here is what it's trying to really say.

There's a point of giving enough energy where the racket begins to drag itself. This is the part where you're supposed to pronate. By bringing your racket frame vertically, there is very little air friction so it can move faster, right at pronation is when the racket begins to drag itself faster than you can therefore adding a lot of power, while making the racket head flat in order to ensure that you hit the ball.

Don't you want to "crack the whip" such that the last segment is at max velocity at (close to) full extension? In that case the torso and shoulders will lead the whip earlier in the motion, but all is square right at the cracking.

In one case, the torso reaches squareness by the time at the same time that the arm has fully extended.

In the other case, the torso reaches squareness before the arm starts its whip. The torso remains square while the arm is whipping (so as to channel its angular momentum into the arm), and the arm then fully extends.

think of an open stance forehand where the hips open up to face square to the net/target before the shoulders do. The hips don't overrotate before contact with the ball. That "braking" of the lower, heavier links in the kinetic chain is what this whipping principle is all about. Without the braking, there would be no channeling of momentum up the chain.

Furthermore, in the serve, it only makes sense to talk of squareness with respect to torso alignment relative to net. When the upper arm reaches extension before the forearm does, doesn't really make sense to say that the upper arm becomes square before the forearm does.

One answer to my question may be that the velocities during the torso-arm link are slow enough that one can engage the chest and shoulder to power the upper arm while piggy backing on the velocity of the twisting torso, rather than use the whip-channeling dynamic.

Well looking at this clip (http://www.youtube.com/watch?v=vcjZ5r_YHV0), it does seem that the shoulders square with the net before the arm comes around and hits the ball. So cracking of the whip seems to be a good way to describe how energy is channeled from the lower body to the arm and hand.

I don't think it's physiologically feasible for the body to completely stop rotating before each segment of the arm starts to crack. One would develop a very awkward and robotic serve which is contrary to the desirable fluidity in a service motion. With that said, angular momentum should still be still conserved even if the prior segment continues to move. I guess not 100% of the energy would be transfered to to ball in the case where the 2nd to last segment is still rotating upon contact. But I would think a lot more energy is wasted due other imperfections in form.
This concept is used in instructions. I've seen a video from the Serve doctor (Pat Dougherty??) where he actually busted out a whip! Otherwise, instructions such as bending your knees, rotation, racquet head drop all eventually lead to this kinetic chain.

Yes you're right, it does appear that there is a squaring of the chest prior to shoulder rotation in that federer serve.

I honestly feel that one should strive to develop their own feel for these things. With enough experimentation, one can find their own balance. It's all about developing a feel for exploding into the ball.

you really do not need to have your chest square at the net in order to whip the arm.
undoubtly, the shoulder should stop (or slow down) in order the transfer the kinetic energy to the upper arm.
there is a way to do it, your left hand, instead of drop to the side, drop to the belly buttom, that will create a small brake for the body rotation, the arm then can whip forward easier.

I don't know, I could be way off, but it's been a while now since I've been feeling that the law of conservation of linear/angular momentum is being used improperly to explain stroke mechanics. These laws only apply to a system which is not being acted upon by external forces.

Consider, for example, the open stance forehand of a righty. The right leg is planted on the ground, and the act of pushing off the legs is applying a force on the system of links in the kinetic chain, and this is present through most of the stroke. The core is effectively "pushing" off the hips which is buttressed by the legs planted firmly on the ground. The next kinetic link then pushes of the previous one and so on. There is no conscious or unconscious attempt to stop any of the links for the purpose of transferring momentum to the next link in the chain. IMO, what is really happening is that the "pushing" of one link loads the next one in the sequence, which is then easier to get moving than if it had to start moving without any support from the previous link. This is not momentum transfer.

The same logic applies to serves also. The core and shoulder stop rotating at some point, IMO, because one hits the limits of one's flexibility, not because of any explicit or tacit attempt to transfer momentum.

Anyway, you can see where I am headed with this reasoning. I am, as always, willing to be enlightened gently...

It looks from the original picture that the black portion would have to move downward to get a whip effect.
If you ever 'snapped' a towel, the snapping seems to come moving the towel backward quickly.
Does this seem right?

I don't know, I could be way off, but it's been a while now since I've been feeling that the law of conservation of linear/angular momentum is being used improperly to explain stroke mechanics. These laws only apply to a system which is not being acted upon by external forces.

Consider, for example, the open stance forehand of a righty. The right leg is planted on the ground, and the act of pushing off the legs is applying a force on the system of links in the kinetic chain, and this is present through most of the stroke. The core is effectively "pushing" off the hips which is buttressed by the legs planted firmly on the ground. The next kinetic link then pushes of the previous one and so on. There is no conscious or unconscious attempt to stop any of the links for the purpose of transferring momentum to the next link in the chain. IMO, what is really happening is that the "pushing" of one link loads the next one in the sequence, which is then easier to get moving than if it had to start moving without any support from the previous link. This is not momentum transfer.

The same logic applies to serves also. The core and shoulder stop rotating at some point, IMO, because one hits the limits of one's flexibility, not because of any explicit or tacit attempt to transfer momentum.

Anyway, you can see where I am headed with this reasoning. I am, as always, willing to be enlightened gently...

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Thanks for the thoughtful post.

There are certainly many things going on in the "kinetic chain" that facilitate efficient power transfer (and generation). Bear in mind I am by no means an expert. The following thoughts are my own amateur insights.

On the most basic level, you have the "piggyback" effect, where the next link simply goes along for the ride. In this case, it doesn't really function as a new link in the chain, but rather functions as a unit with the previous link.

An example of this would be turning the hips and shoulders together as a single unit, but driving the motion solely through power generated in the muscles that control the hips.

Then you have the conservation of angular momentum effect, which is when a previous and heavier link slows down and as a result transfers the momentum to the higher and lighter set of links. The braking can happen through conscious joint locking, natural joint constraints, or countermovements (for example the role of the left arm in the right handed 1hbh, or the scissor kick where the right leg kicks backwards during the right handed open stance forehand. In both these countermovements, the limb in question prevents the hips from overrotating, allowing better balance and efficient transfer of momentum up to the shoulder and arm).

Then you have independent torque generation at each link. So once the hips stop moving, the upper torso naturally starts to swing, but can be turbo boosted with extra power from the muscles that control the torso swing. This is likely utilized in situations where the velocities and forces are low enough that independent torque generation won't slow things down. In the case of radial deviation of the wrist during the final portion of the serve, a loose wrist facilitates passive torque transfer without any independent power generation that could interfere with the motion. In the case of the link between hips, torso, and shoulder in the 1hbh, I'm almost certain that independent power generation in the abduction of the shoulders can add this turbo boost effect.

Finally you have the stretch reflexes in the muscle, and the natural elasticity of the muscle. This probably comes into play when you have a combination of passive chanelling of momentum as well as active torque generation.

Figuring out which dynamics are at play in which strokes and during which elements of each stroke is a tricky proposal indeed!

It looks from the original picture that the black portion would have to move downward to get a whip effect.
If you ever 'snapped' a towel, the snapping seems to come moving the towel backward quickly.
Does this seem right?

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I don't know enough about whip dynamics and whip waves to fully answer your question, but yes, that backwards motion before the snap does seem to increase power. Probably more relevant in the case where you are generating a true continuous wave. In the example I illustrated, if anything it is more of an approximation of a whip wave.

Nevertheless, wave or not, the figure still illustrates the conservation of angular momentum principle. You will get a successively faster joint motion as you move up the three links.

And yes, you would have to start rotating the black piece from a non-locked position (and in the figure it's already in locked position).

Figuring out which dynamics are at play in which strokes and during which elements of each stroke is a tricky proposal indeed!

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My gut feel is that momentum transfer itself plays a minimal role. I tend to think that the primary contributors are, (1) the stretch contraction reflexes that kick in when abrupt movement of one link loads the next one in the chain, and (2) the torque developed by the joint. Of course, each link always "piggybacks" on the previous one, as you have aptly put it.

I only point this out because I think there is too much acceptance of the momentum transfer theory, and if people actually try to stop hip or shoulder rotation midstream to get racquet head speed, they will surely hurt themselves...

I don't know enough about whip dynamics and whip waves to fully answer your question, but yes, that backwards motion before the snap does seem to increase power. Probably more relevant in the case where you are generating a true continuous wave. In the example I illustrated, if anything it is more of an approximation of a whip wave.

Nevertheless, wave or not, the figure still illustrates the conservation of angular momentum principle. You will get a successively faster joint motion as you move up the three links.

And yes, you would have to start rotating the black piece from a non-locked position (and in the figure it's already in locked position).

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The whip is a very coarse analogy to serve mechanics, IMHO. A whip, because of its flexibility, is capable of sustaining a wave that operates on a continuously reducing amount of mass, and so when the initial momentum is transferred to the relatively small amount of mass near the tip, it will cause the tip to move very fast to maintain the initial momentum and thus cause the cracking effect as it breaks the sound barrier. The arm, however, has three joints where it is flexible - shoulder, elbow, and the wrist. There is no question of the upper arm or forearm being able to sustain a wave, because they are not that flexible! The whip analogy therefore cannot apply literally, I believe, and torque developed at the joints will be the dominant factor in creating racquet head speed. The whip is a great visualization, however. IMHO, of course!

True, I believe I may have inadvertently conflated whip physics with the angular momentum channeling principle, simply because I first heard about the principle in that whip physics paper.

That said, I think when it comes to the high velocities involved in service mechanics, the angular momentum principle comes into play especially at the wrist.

There's an interesting thread where this was discussed in quite some depth. I reference one study where a nerve blocking agent was administered to the triceps of throwers. There was little effect upon throwing performance despite this, suggesting a passive role of the elbow joint in throwing.

Here's the thread (I've linked it to a post I made half way through it. The discussion gets interesting towards the end. Brian Gordon, John Yandell, and Dave Smith contribute also).

the consensus seems to be that there is probably complete passivity at the wrist joint, so pure momentum channeling, or what Brian Gordon calls "motion dependent torque". (Gordon remains agnostic on the passivity of the wrist joint due to lack of empirical data that answers the question definitively, but seems to lean towards it, like Yandell, based on observation and experience).

In fact, the point about conservation of momentum I am drawing upon is only briefly mentioned in the intro to the paper. The bulk of the paper has little relevance to this thread.

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Isn't this coming from someone who didn't read the entire article?

The most efficient way to crack a whip, in
terms of producing the loudest crack for the least amount of effort, is to send a planar loop down a tapering rod with
extra applied tension to provide further acceleration.

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That's from the article. With a slight knowledge (I'm minoring in it) of physics, you do know that this is an efficient way to get most energy from it, and energy leads to power.

Why doesn't serve instruction encourage this delayed cracking of the whip principle between torso and arms?

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The crack itself is a sonic boom created when a section of the whip at its tip travels faster than the speed of sound.

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As I previously stated, there is a certain point in which racket head speed travels faster than you can make it, and believe me, humans cannot travel faster than the speed of sound so this article is very relevant to your question and what I have stated.

This principle can be used in cracking the whip of the arm, but my question is whether it should also be used to channel momentum from the torso to the arms.

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Power comes from all of your bent joints, each and every one of them.

As for the picture, the wood stops at a certain point and some of the energy is given back to the origin, and our torso's absorb a LOT of energy (hence seat belts go around the torso) which would only deter stronger serves so as the author of the article stated, tension (in our case, string tension) does make a difference.

I read enough of it to understand that you didn't summarize it. Are you seriously suggesting that you read the entire thing, understood it, and captured it with a paragraph that was only tangentially related to a small point made in the intro to the paper?

I'm just calling you on the bs man

As I previously stated, there is a certain point in which racket head speed travels faster than you can make it, and believe me, humans cannot travel faster than the speed of sound so this article is very relevant to your question and what I have stated.

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Power comes from all of your bent joints, each and every one of them.

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These two statements appear to contradict each other. If the racquet is travelling faster than the wrist can power it, then the wrist is passive, and power is coming from lower links in the chain, not from the joint.

I read enough of it to understand that you didn't summarize it. Are you seriously suggesting that you read the entire thing, understood it, and captured it with a paragraph that was only tangentially related to a small point made in the intro to the paper?

I'm just calling you on the bs man

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No one's going to read all of that. Especially me, I'm from ASU, and looking at a medical school writing about physics in comparison to a business/science school:

I don't mean the wrist joint, I mean all bent joints in your body. These are places where two things can happen:

Energy can be stored.
Energy can be released.

Energy is usually "stored" for these shots like drop shots.

In this situation for serves, we are releasing energy for spin and power. The power then begins to bend more at certain joints and eventually releases on the racket by going through all major joints from legs to wrist.

Improper serve technique can put some of that energy back to you. Although torso's are enough to withhold certain car crashes, the arms, elbows are much weaker, and over years of wear and tear it degrades and causes injuries as we've seen many of.

True, I believe I may have inadvertently conflated whip physics with the angular momentum channeling principle, simply because I first heard about the principle in that whip physics paper.

That said, I think when it comes to the high velocities involved in service mechanics, the angular momentum principle comes into play especially at the wrist.

There's an interesting thread where this was discussed in quite some depth. I reference one study where a nerve blocking agent was administered to the triceps of throwers. There was little effect upon throwing performance despite this, suggesting a passive role of the elbow joint in throwing.

Here's the thread (I've linked it to a post I made half way through it. The discussion gets interesting towards the end. Brian Gordon, John Yandell, and Dave Smith contribute also).

the consensus seems to be that there is probably complete passivity at the wrist joint, so pure momentum channeling, or what Brian Gordon calls "motion dependent torque". (Gordon remains agnostic on the passivity of the wrist joint due to lack of empirical data that answers the question definitively, but seems to lean towards it, like Yandell, based on observation and experience).

edit: just realized - you already contributed to that thread bhupaes!

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Ah, well - the wrist is another matter, and pretty much everything we know know about it has been summarized in the thread you have referenced. I will leave that topic alone for now! As the saying goes, fools venture where angels fear to tread, and I don't want to look foolish...

Although I am very big on the whip analogy in serving and have talked about it on these boards, your drawing and the serve motion are probably closer to multiple catapults. Force is applied at each catapult in the system and the best result is when the forces are timed correctly. (Not like a whip where force is applied only at the base) Since the wrist has comparatively little force imparted to it and is so flexible, it may act more whip-like than the other joints.

I am not qualified to get into the deep biomech discussion here, but I will make this observation. Vitually no top male server--Roddick, Sampras, Federer, you name him, has the shoulders open or parallel to the baseline at contact.

This seems to be a clear sequence in the rotation of the torso in relationship to the upward motion of the arm to the contact. The shoulders are more closed in the ad, relative to the baseline, but still closed in both courts. We are doing a study of Sampras that will measure these angles and also the hip and shoulder speeds.

interesting John, thanks for sharing this. I can see how in the ad court one wouldn't want to square the shoulders with the net, but rather with the target, but I would have thought, based on my naive intuition, that in the deuce court the shoulders have rotated even more past square with the net, so that they're square with the target.

I'm still learning about the biomechanics (based on Brian Gordon's articles on your website), and still have much to learn about the alignment of the body depending on whether one is serving to duece court or ad court.

If so, then wouldn't it make sense to have the shoulders and chest square with the net/target before the arm starts to crack? So long as you prevent the torso from overrotating, and "apply the brakes", then that momentum will be channeled into the arm.

Why doesn't serve instruction encourage this delayed cracking of the whip principle between torso and arms?

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The instructions do encourage the torso rotation, except that you have the wrong image. The torso is supposed to rotate vertically, aka shoulder roll, not horizontally as in the forehand. As you can imagine if you rotate the torso vertically, then the shoulders will remain sideways. That's why the instructions tell you to make sure that you don't open the shoulders. Of course, the instructions could tell you to rotate the torso vertically, not horizontally, but then, they wouldn't be the complete garbage that they are, no?

The instructions do encourage the torso rotation, except that you have the wrong image. The torso is supposed to rotate vertically, aka shoulder roll, not horizontally as in the forehand. As you can imagine if you rotate the torso vertically, then the shoulders will remain sideways. That's why the instructions tell you to make sure that you don't open the shoulders. Of course, the instructions could tell you to rotate the torso vertically, not horizontally, but then, they wouldn't be the complete garbage that they are, no?

Good point about the additional rotations. The shoulders actually rotate 3 ways. Somersault, and shoulder over shoulder, and then around the axis.

Just one of the complexities. There are two questions, what are the motions and the key positions--how do players recreate them. My own views are that if the stance, leg action, toss, and upward arm action are correct, the shoulders will tend to take care of themselves. With video you can compare the 3 types of rotation to good models and then try to figure out how to push your motion toward that.

Ok, so first an observation I've made regarding how to serve properly. I've often heard it said that the shoulders should be square with the net at the same time that the arm reaches full extension. The idea is that alignining the timing of the shoulder/chest turn with the timing of the arm extension allows for most efficient power transfer to the ball.

One of the posters here (jollyroger) even posted side by side comparison photos of his serve vs. another poster's serve which illustrated this beautifully.

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I think Whip Effect Theory cannot be used to describe a tennis serve. In theory, they assume, there is only one active element – the handle. But, any limb of the body is active. Each of them has at least one joint and a hundreds of muscles. Each of this muscle can be treated as handle as well. How can our brain provide synchronization of all of these (hundreds) handles to make our body to follow this theory.For example, if we tied three handle to the one whip and ask three people use them at the same time to produce cracking effect, I believe nothing happens. I made the experiment for forehand stroke. I kept my right arm relaxed and rotated my torso, hips, and shoulders as fast as possible. I created very weak whip effect and pitiful forehand.

one other thing to take into consideration is the stretch reflex that is
triggered in each chain. In an ideal serve, you can trigger this to serve
as a "booster rocket" to help accelerate and build speed in each link.
One of the reasons why at as you coil on your serve you don't want to
go to maximum range of motion (maximum coil). I think you almost
want a little room/leeway. That's my theory.

My current understanding, which has been updated since I created this thread, is that you're partially right.

I don't think that the conservation of angular momentum principle plays as much a role between torso and arm as it does within the arm itself.

As for your comments about the brain synchronizing muscles with such perfect timing, that is completely possible. The beauty of neural networks is that they don't need to explicitly calculate things - they learn through experience: trial and error + quality feedback allows for some very sophisticated problem solving.

Consider the amount of fine muscular control needed to simply walk and remain balanced. From a very early age in life we achieve this with as little effort as it takes to breathe; yet if you were to analyze all the different muscles needed to be activated, the timing needs to be fairly exquisite.

Also, there's a large component of feedback from the system as a whole that aids in this timing, in addition to pure mechanics.

As an example of mechanics, consider what happens when you rapidly extend your elbow joint with a loose wrist. The elbow joint reaches its anatomical limit naturally, and the momentum gets channeled into the wrist which then flexes. In this case, you don't even need muscular timing to time the flexion of the wrist - it happens as a consequence of natural mechanics.

As an example of feedback from other parts of the system (other than the brain), consider basic reflexes - for example have you ever walked barefoot and stepped on something sharp and very quickly adjusted your weight to avoid penetration? A lot of those muscles are coordinated by local circuits that are independent of the brain.

I see no reason that similar principles can aid with learned complex movements, but of course this is speculation.

not sure - only been in the game since last august, and haven't really been motivated to find one. I prefer the internet and self discovery for now... (assuming you're talking about teaching pros right?).

I can ask around though - I have some indirect connections to high level players and coaches.

one other thing to take into consideration is the stretch reflex that is
triggered in each chain. In an ideal serve, you can trigger this to serve
as a "booster rocket" to help accelerate and build speed in each link.
One of the reasons why at as you coil on your serve you don't want to
go to maximum range of motion (maximum coil). I think you almost
want a little room/leeway. That's my theory.

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Interesting. I don't know much about the stretch reflex (something to do with golgi tendons or something right?), but I always assumed it was activated when you stretched the muscle to a large degree. But you seem to be implying that when you stretch the muscle too much (maximum coil), the reflex doesn't occur?

I played for three or four years as a kid - had a buddy who I used to hit around with. Didn't take lessons and didn't know a forehand grip from a backhand grip but developed decent hand eye coordination and a feel for the racquet and ball. Played about once a year between then and the age of 32 (last year), which is when I decided I wanted to take up the game and learn it.

Those years as a kid definitely helped in some ways though - also having a good throwing arm helped tremendously in the serve.

I played for three or four years as a kid - had a buddy who I used to hit around with. Didn't take lessons and didn't know a forehand grip from a backhand grip but developed decent hand eye coordination and a feel for the racquet and ball. Played about once a year between then and the age of 32 (last year), which is when I decided I wanted to take up the game and learn it.

Those years as a kid definitely helped in some ways though - also having a good throwing arm helped tremendously in the serve.

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serves are easy

i came to that conclusion because a lot of WTA has technically sound serves. their forehands all stink